The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Kod yang boleh dibaiki secara tempatan, yang boleh membaiki simbol yang dipadamkan daripada simbol lain, telah menarik perhatian ramai sejak beberapa tahun kebelakangan ini kerana harta pembaikan tempatannya berkesan pada sistem storan teragih. (ru, δu)u∈[s]-kod yang boleh dibaiki secara tempatan dengan berbilang lokaliti, yang merupakan lanjutan daripada kod biasa yang boleh dibaiki tempatan, boleh membaiki δu-1 simbol dipadamkan serentak daripada set yang mengandungi paling banyak ru simbol. Sempadan atas pada jarak minimum kod ini dan kaedah pembinaan kod optimum, mencapai terikat ini dengan kesaksamaan, diberikan oleh Chen, Hao, dan Xia. Dalam makalah ini, kami membincangkan sekatan parameter pembinaan sedia ada, dan kami mencadangkan pembinaan eksplisit kod optimum dengan berbilang lokaliti dengan sekatan santai berdasarkan polinomial pengekodan yang diperkenalkan oleh Tamo dan Barg. Pembinaan yang dicadangkan boleh mereka bentuk kod yang jarak minimumnya tidak dapat direalisasikan oleh pembinaan sedia ada.
Tomoya HAMADA
University of Electro-Communications
Hideki YAGI
University of Electro-Communications
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Salinan
Tomoya HAMADA, Hideki YAGI, "Construction of Locally Repairable Codes with Multiple Localities Based on Encoding Polynomial" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 12, pp. 2047-2054, December 2018, doi: 10.1587/transfun.E101.A.2047.
Abstract: Locally repairable codes, which can repair erased symbols from other symbols, have attracted a good deal of attention in recent years because its local repair property is effective on distributed storage systems. (ru, δu)u∈[s]-locally repairable codes with multiple localities, which are an extension of ordinary locally repairable codes, can repair δu-1 erased symbols simultaneously from a set consisting of at most ru symbols. An upper bound on the minimum distance of these codes and a construction method of optimal codes, attaining this bound with equality, were given by Chen, Hao, and Xia. In this paper, we discuss the parameter restrictions of the existing construction, and we propose explicit constructions of optimal codes with multiple localities with relaxed restrictions based on the encoding polynomial introduced by Tamo and Barg. The proposed construction can design a code whose minimum distance is unrealizable by the existing construction.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.2047/_p
Salinan
@ARTICLE{e101-a_12_2047,
author={Tomoya HAMADA, Hideki YAGI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Construction of Locally Repairable Codes with Multiple Localities Based on Encoding Polynomial},
year={2018},
volume={E101-A},
number={12},
pages={2047-2054},
abstract={Locally repairable codes, which can repair erased symbols from other symbols, have attracted a good deal of attention in recent years because its local repair property is effective on distributed storage systems. (ru, δu)u∈[s]-locally repairable codes with multiple localities, which are an extension of ordinary locally repairable codes, can repair δu-1 erased symbols simultaneously from a set consisting of at most ru symbols. An upper bound on the minimum distance of these codes and a construction method of optimal codes, attaining this bound with equality, were given by Chen, Hao, and Xia. In this paper, we discuss the parameter restrictions of the existing construction, and we propose explicit constructions of optimal codes with multiple localities with relaxed restrictions based on the encoding polynomial introduced by Tamo and Barg. The proposed construction can design a code whose minimum distance is unrealizable by the existing construction.},
keywords={},
doi={10.1587/transfun.E101.A.2047},
ISSN={1745-1337},
month={December},}
Salinan
TY - JOUR
TI - Construction of Locally Repairable Codes with Multiple Localities Based on Encoding Polynomial
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2047
EP - 2054
AU - Tomoya HAMADA
AU - Hideki YAGI
PY - 2018
DO - 10.1587/transfun.E101.A.2047
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2018
AB - Locally repairable codes, which can repair erased symbols from other symbols, have attracted a good deal of attention in recent years because its local repair property is effective on distributed storage systems. (ru, δu)u∈[s]-locally repairable codes with multiple localities, which are an extension of ordinary locally repairable codes, can repair δu-1 erased symbols simultaneously from a set consisting of at most ru symbols. An upper bound on the minimum distance of these codes and a construction method of optimal codes, attaining this bound with equality, were given by Chen, Hao, and Xia. In this paper, we discuss the parameter restrictions of the existing construction, and we propose explicit constructions of optimal codes with multiple localities with relaxed restrictions based on the encoding polynomial introduced by Tamo and Barg. The proposed construction can design a code whose minimum distance is unrealizable by the existing construction.
ER -